Performance Approximation of Compressive Sensing Multi-User Detection via Replica Symmetry

Compressive Sensing Multi-User Detection (CS-MUD) is a recently developed physical (PHY) layer technique [1] to support Massive Machine Communication (MMC) in the next generation of mobile communication (5G) [2], [3]. CS-MUD has been investigated in joint Medium Access Control (MAC) and PHY layer protocol design [4], [5] but the lack of analytical performance description makes the joint design cumbersome. To expand the joint MAC- and PHY-layer protocol design considering a larger parameter space and to gain insights in the cross-layer optimization, we present a performance abstraction for CS-MUD to avoid extensive numerical simulation. Within this work, we exploit a low-complexity approach to approximate the performance of CS-MUD through the Replica Symmetry in large system analysis [6].